CBSE Class 11 (Commerce) Mathematical Induction — practice questions
35 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice CBSE Class 11 (Commerce) Mathematical Induction in the app →In a proof by induction, which part is established first?What is the assumption made in the induction step called?Which everyday metaphor is used to explain mathematical induction?If P(1) is true and P(k) implies P(k + 1), P(n) holds for what?Does mathematical induction give a probable conclusion or a proof?To prove a statement for all n that are at least 5, which base case is used?Who gave the first explicit formulation of the induction principle in 1665?Around 1000 AD, who wrote the earliest implicit proof by induction?The sum of the first n odd integers, shown by induction, equals what?A staircase has 20 numbered steps. What is 1 + 2 + 3 + ... + 20?Which method, used by Fermat, is a variation of induction?In strong induction, the step assumes the claim for which cases?How do weak and strong induction compare in what they can prove?Strong induction proves every integer above 1 is a product of what?Which amount cannot be made from 4- and 5-dollar coins?The all-horses-one-color induction argument fails in which part?Who proposed the false argument that all horses share one color?Cauchy extended the AM-GM inequality from powers of 2 to all n by what?Induction extended to trees and similar structures is called what?In which century did the modern formal treatment of induction arrive?Which Swiss mathematician employed the induction hypothesis early on?To prove 1 + 3 + ... + (2k - 1) = k squared, which term moves P(k) to P(k + 1)?For 1 + 2 + ... + n = n(n + 1)/2, what is the right side of P(k + 1)?Using the formula n(n + 1)(2n + 1)/6, find 1 squared + ... + 10 squared.The sum of cubes 1 to n equals [n(n + 1)/2] squared. What is 1 cubed to 6 cubed?If 2 + 4 + ... + 2n = n(n + 1), what is the sum for n = 12?The sum of 1/(k(k + 1)) for k = 1 to n is n/(n + 1). What is it for n = 9?For every natural n, 7^n - 1 is divisible by which number?What is the least n from which n! > 2^n holds for all larger n too?For 2^n >= n + 5, which base case value of n is used?In prefix induction, a number's prefix is formed by doing what?Predecessor induction is an n-step loop; prefix induction matches what?Backward induction needs the statement proved for what kind of set?In the ladder metaphor, the base case corresponds to what?Mathematical induction is closely related to which computing idea?